"""Given the following details of a matrix with n columns and 2 rows :

The matrix is a binary matrix, which means each element in the matrix can be 0 or 1.
The sum of elements of the 0-th(upper) row is given as upper.
The sum of elements of the 1-st(lower) row is given as lower.
The sum of elements in the i-th column(0-indexed) is colsum[i], where colsum is given as an integer array with length n.
Your task is to reconstruct the matrix with upper, lower and colsum.

Return it as a 2-D integer array.

If there are more than one valid solution, any of them will be accepted.

If no valid solution exists, return an empty 2-D array.

 

Example 1:

Input: upper = 2, lower = 1, colsum = [1,1,1]
Output: [[1,1,0],[0,0,1]]
Explanation: [[1,0,1],[0,1,0]], and [[0,1,1],[1,0,0]] are also correct answers.
Example 2:

Input: upper = 2, lower = 3, colsum = [2,2,1,1]
Output: []
Example 3:

Input: upper = 5, lower = 5, colsum = [2,1,2,0,1,0,1,2,0,1]
Output: [[1,1,1,0,1,0,0,1,0,0],[1,0,1,0,0,0,1,1,0,1]]
 

Constraints:

1 <= colsum.length <= 10^5
0 <= upper, lower <= colsum.length
0 <= colsum[i] <= 2"""

class Solution {
public:
    vector<vector<int>> reconstructMatrix(int upper, int lower, vector<int>& colsum) {
        int two = 0;
        int sum = 0;
        for (int it : colsum) {
            if (it == 2) {
                two++;
            }
            sum += it;
        }
        if (sum != upper + lower) return {};
        upper -= two;
        lower -= two;
        if (min(lower, upper) < 0) {
            return {};
        }
        vector<vector<int>> res(2, vector<int>(colsum.size(), 0));
        for (int i = 0; i < colsum.size(); i++) {
            if (colsum[i] == 2) {
                res[0][i] = res[1][i] = 1;
            } else if (colsum[i] == 1) {
                if (upper > 0) {
                    res[0][i] = 1;
                    res[1][i] = 0;
                    upper--;
                } else {
                    res[0][i] = 0;
                    res[1][i] = 1;
                }
            }
        }
        return res;
    }
};